中等Reynolds数下并列方柱统流的数值模拟──MAC－AF1方法及其应用

本文通过采用ＭＡＣ－ＡＦ１方法求解原始变量二维不可压非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，对中等Ｒａｙｎｏｌｄｓ数绕流下的并列方柱绕流进行了数值模拟。通过对Ｒｅ＝３００、５００、１０００、２０００及间隙度为ｓ／ｈ＝２．３时并列方柱的数值计算表明：Ｒｅ数对横向力的变化频率毫无影响，恰好是单方柱绕流横向力变化频率的两倍。阻力的频率与横向力的频率相同，阻力的时间平均值基本上与Ｒｅ数无关，但随着Ｒｅ数的增大，阻力和横向力随时间变化的波动幅度稍微有所增加。本文计算的方柱阻力时间平均值和横向力的频率与实验值符合得很好。     

基于通量差分分裂型上风差分方法求解非定常不可压缩 Navier-Stokes 方程

本文使用通量差分分裂型上风差分格式求解了三维非定常不可压缩 Ｎａｖｉｅｒ Ｓｔｏｋｅｓ方程。采用这种方法，本文首先在绝对和相对两种参考系中数值模拟了低雷诺数非定常条件下平板周期性振荡问题，计算结果与解析解相当吻合；然后数值考察了雷诺数 Ｒｅ ＝ ２００，角速度 ω＝ ０和 ω＝ １ 两种情形下圆柱绕流问题，数值计算所得的阻力系数、升力系数和斯特罗哈数同试验结果完全相符。     

基于通量差分分裂型上风差分方法求解非定常不可压？…

本文使用通量差分分裂型上风差分格式求解了三晨定常不可压缩ＮＨａｖｉｅｒ－Ｓｔｏｋｅｓ方程。采用这种方法，本文首先在绝对和相对两种数值模拟了低雷诺数定常条件下平板周期性振荡问题，计算结果与解析解相当吻合；然后数值考察了雷诺数Ｒｅ＝２００，角速度ω＝０和ω＝１两种情形下圆柱绕流问题，数值计算所得的阻力系数力系数和斯特罗哈 试验结果完全相符。     

二维突扩层流的开边界问题

以混合有限分析法结合相应的边界条件对二维突扩层流进行了Ｒｅ＝５６和１１４流动的计算，得出与试验资料十分吻合结果，发现Ｒｅ＝５６时流动是对称的，而Ｒｅ＝１１４时主流偏向一侧。同时对其开边界条件也进行了数值分析，得出计算区域应满足的最短距离。     

低Reynolds数横向排列双圆柱绕流的POD-Galerkin谱方法数值模拟

该文将恰当正交分解(POD)方法应用到低Reynolds数(Re)二维横向排列双圆柱绕流问题.采用Fluent数值模拟得到Re=90时的流场数据库,在此基础上采用snapshot的方法构造了POD基.基于此POD基,构造了求解二维不可压缩Navier-Stokes方程组的低维Galerkin谱方法.采用该低维数值模拟方法,再现了低Reynolds数横向排列双圆柱绕流的多种复杂流动模式,其结果与已有的高精度直接数值模拟的结果符合较好,而计算量却非常小,显示了POD方法的有效性和优越性.     

特征线法分析长距离输油管道的流动瞬变过程

本文建立了基于特征线方法求充动瞬变过程的数值模型，编制了针对长距离输油管道流动瞬变过程的分析软件。在数值处理上，Ｄａｒｃｙ＝Ｗｅｉｓｂａｃｈ摩擦力项用二阶精度格式来近似，因此保证了高粘度流体在流动瞬变过程分析时的计算稳定性和精确度。模型考虑了埋管地形对沿线瞬变压力的影响，当某一泵站发生水击后其它站的反应同其上控程序确定。应用该软件，分析模拟了某一长距离输油管道在中间泵站停电或末站瞬时关阀情况下的流     

粘性流体圆柱绕流的混合有限分解析

应用混合有限分析法拟合坐标系对粘性流体圆柱绕流进行了数值计算，得出Ｒｅ〈４０形成的分离区长度和分离角同试验资料吻合很好。也计算了Ｒｅ＝１００和２００时，旋涡的形成和脱落，算得的脱落斯特罗哈数分别为０．１６和０．１９，同试验结果完全相符。     

BINGHAM液体在圆管中流动的稳定性

将涡流模型［１］推广应用于研究一类带屈服应力的液体－Ｂｉｎｇｈａｍ液体在圆管中流动的稳定性，建立了判别其流动状态的判据──广义临界雷诺数Ｒｅｃ。同时将Ｍｉｓｈａ—Ｔｒｐａｔｈｉ［２］和ＨａｎＫｓ［３］流动稳定性理论用于该问题的研究。各模型的研究结果与Ｆｒｏｉｓｈｔｅｔｅｒ＆Ｖｉｎｏｇｒａｄｏｖ提供的实验数据［４］进行了比较。理论分析与实验资料表明：涡流模型对于非牛顿流体的流动稳定性研究具有较好的适应性与准确性     

粘弹性流体在盲端孔隙中的流场

以带有盲孔的流道模拟油藏中的盲端孔隙，应用数值方法研究了上随体Maxwell流体在盲端孔隙中的流动特性。着重分析了流体流变性和盲端倾角对流场的影响规律。计算结果表明，驱替液的粘弹性是影响盲端波及效率的重要因素；在较大的盲端倾角范围内，低雷诺数（Re）流动条件下，流体的威森博格数（We）越大，孔隙盲端中的流动区域越大，滞留区越小。     

方柱绕流CFX三维数值模拟

该文利用计算流体力学软件CFX,对恒定来流条件下黏性不可压缩流体的圆柱和方柱绕流进行了数值模拟。采用有限体积法和SIMPLE计算方法,求解不可压缩Navier-Stokes方程。首先开展雷诺数(Re)等于100和300时的圆柱和方柱绕流问题的二维数值模拟,分析比较了网格大小和时间步长对模拟结果的影响,并比较了不同柱体情况下的流体流动的差异性。进而对Re=100、300时方柱绕流问题进行了三维数值模拟,重点分析了各截面上阻力和升力系数、Strouhal数以及涡量特性与二维结果的差异。发现Re=300时,周向压力、速度场和涡量场与Re=100时相比存在明显的三维特性,并且由于二维流动结构发展成三维流动结构时需要消耗能量,导致三维的阻力升力系数计算结果均小于二维计算结果。研究表明,该文的数值结果与文献结果吻合良好。     

SUPG方法解粘弹性流动问题

高Ｗｉ数下粘弹性流动的数值模拟一直是一个比较困难的研究领域，这主要是因为控制方程类型向双典型转变，常规Ｇａｌｅｒｋｉｎ有限元不适用于离散双曲型问题，计算结果产生失真振荡。本文采用原始变量的Ｎ－Ｓ方程和Ｏｌｄｒｏｙｄ－Ｂ本构方程，采用ＳＵＰＧ方法离散本构方程，计算了绕圆管内一珠的流动。计算结果表明，ＳＵＰＧ方法可以成功地用于离散本构方程，使计算的极限Ｗｉ数达到１．９。     

NUMERICAL SIMULATION OF FLOWS FOR SECOND-ORDER VISCOELASTIC FLUID COUPLED WITH HEAT TRANSFER BY DIFFERENTIAL QUADRATURE METHOD

The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered. A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zerothorder and first-order approximate governing equations were obtained by means of the perturbation method. To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain. The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM). The matching conditions at the interface between the inner and outer domains were presented. An iterative method for solving these discretized equations was given in this paper. The numerical results obtained agree with existing results.     

FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.     

NUMERICAL INVESTIGATION ON NON-NEWTONIAN FLOWS THROUGH DOUBLE CONSTRICTIONS BY AN UNSTRUCTURED FINITE VOLUME METHOD

This article presents a numerical investigation on a steady non-Newtonian flow through a two-dimensional channel with double constrictions. The power-law mode is employed in describing the non-Newtonian behavior of the flow. An unstructured finite volume method combined with a fractional-step projection method is developed for the discretization of incompressible equations governing the non-Newtonian flows. The important flow dynamics related with the arterial diseases, such as the wall shear stress and vortex generation, are also numerically studied in detail. Numerical results reveal that there are marked differences between Newtonian and non-Newtonian models.     

NUMERICAL COMPUTATION OF PRESSURE GRADIENT FOR THE FLOW OF POWER-LAW FLUID IN ANNULUS WITH INNER CYLINDER EXECUTING A PLANETARY MOTION

With the governing equations for the flow of the power-law fluid in annulus with the inner cylinder executing a planetary motion being transformed by using the undetermined coefficient method, the formula of pressure gradient for this flow under the given flow rate and the relevant numerical calculation method are given in this article. Through the experiments on the flow of Hydrolyzed Polyacrylamide (HPAM) aqueous solution which can be regarded as a power-law fluid, the calculated results of the pressure gradient values are compared with measured data, the mean relative error between them is smaller than 5%, which verifies the results presented in this article.     

Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface

In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail.     

两层黏性流体中直立圆柱体绕流的三维数值模拟

研究了两层流体中直立贯底圆柱体的三维黏性绕流问题.以不可压缩Navier-Stokes方程为控制方程,应用VOF方法追踪两层流体的内界面,建立了该问题的数值模拟方法.成功地数值模拟了两层流体中圆柱体黏性绕流产生的三维尾涡特征,表明了流体的密度分层效应对直立贯底圆柱体的尾涡特性和阻力系数都是有影响的.在海洋立管涡激振动的研究中,考虑流体的密度分层效应是重要的.     

挟沙水流中石油类污染物输移转化的数值模拟

利用一维数学模型模拟了挟沙水流中石油类污染物输移转化现象。在所使用的数学模型中引入了基于固-液两相流基本守恒关系得到的吸附态、溶解态污染物输移转化方程,用以反映泥沙运动、河床冲淤与污染物输移转化的强耦合过程。文中对水槽及天然河流中石油类污染物输移过程的模拟结果表明,本文结果较好地反映了泥沙运动、河床冲淤对污染输移的影响,可用于挟沙水流中石油类污染物输移转化的模拟。     

Numerical Simulation of Two-Dimensional Dam-Break Flows in Curved Channels

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

底部加热的两板间水平流动进口段流动特性分析

采用二维流体力学基本方程组对普朗特数Pr=0.72的具有水平流动的底部加热两板之间的流动特性进行数值模拟。结果表明,对于给定相对瑞利数r,随着雷诺数Re的增加,底部加热的两板之间依次出现定常对流滚动,均匀行波对流滚动,具有水平流动进口段的局部行波对流滚动及水平流动。对于相对瑞利数r=3,在雷诺数9.0＜Re＜21.0范围内,系统是局部行波对流滚动,存在水平流动进口段。随着雷诺数增加,水平流动进口段长度增加。对于雷诺数Re=25.0,在相对瑞利数4＜r＜12范围内,两板之间是局部行波对流滚动,出现水平流动进口段。随着相对瑞利数增加,水平流动进口段长度减小。最后给出了进口段长度随雷诺数或相对瑞利数变化的经验式。